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but what is the avail of this formula and what is its significance?

      But without it the Fermat Last Theorem will remain unproven!

      Yeah… would Fermat really hide such a treasure from everyone?

      Well, that's a good question. Anyway, the plot is already twisted in the right direction and quite famously … although this is not even the beginning and only a light aperitif, but it acting already is oh so good!

      Is it true that a lot of money was promised for this theorem?

      Hmm, promised – yes, and even paid … but not at all for the FLT!

      How is this so, and for what?

      For the error, that was revealed in the proof, but science did not want notice it for 25 years.

      So, it turns out all this work with our book will go past the cash box?

      Well, that's another good question. However, it has already long been known that for science money is not paid. Well, if … as if for … doing science … or taking care of it … well, for the good of the state, then yes, billions are spinning here, but the very science has never existed and does not exist now.

      So perhaps we need to do something incredible here in this book so that we can get something out of these billions?

      But no, then no one will read this book, besides all the places of the distribution of money have long been occupied. It is necessary to do this book with real science, but for this we need to use special approaches and principles. Particularly, the main principle should be that all the topics touched upon here contain secrets, and such that they are hidden not otherwise … as it is said … ah yes, behind seven seals!

      Wow, it’s light to say…

      Moreover, about this should be announced in advance (we are now doing this) that even in relatively calm places of narration no one should have any doubt that in every topic something must necessarily be very much surprise or even shake! Well, not literally, of course. Say, it is given in some place a calm explanation of some entity or their components and suddenly, unexpectedly … bubuh!!! And it turns out that here the amazing secret is hiding, which was lurking under the guise of what has been known for a long time, but did not attract any attention. Another principle is that of all the secrets we have revealed (and there are more than a hundred of them here!!!) we must leave some share (say, one and half dozen) as undisclosed. Otherwise the children will be offended that them no one nothing left for their own discoveries …

      !!!… What?… The children???

      Oh yes, we narrowly forgot to say that this book is largely childish. Most adults would be unable to retrain for a such a thorough science. It is clear, they will very offended hearing this, but we of course will not trumpet about it over the entire world, and even will observe decency i.e. from all the tasks of basic science that we will discuss, only the lightest will be singled out specifically for children. They’ll be happy about this because among these tasks there will be … the very FLT!!! Yes, it is in this book of ours that for the first time in the entire history of the FLT, this problem, and not just a problem, but one of the fundamental basics of science (!!!) will be solved in expanded form together with some other problems related to it. In this sense, the FLT will be our guiding star and its first-discoverer Pierre Fermat will be our mentor from whom we will directly (!) receive all the information we need.

      However, the FLT is only one of a whole hundred (!!!) tasks that will also receive solutions here for the first time! Along with the solution of the FLT problem, there will be a whole heap of other very impressive tasks that will delight many kids and interest them for a long time. And we will try very hard to get their attention, then they also will draw adults into this game. If we compare the significance of the tasks solved here, the undisputed leadership will remain by the FLT although as for the difficulty of its solving, it is quite simple and secondary school students can easily cope with it … Do you doubt? But still this is a task from the 17th century, however today's ones will be more difficult, but in order to solve them, you need to have a reliable foundation of knowledge and FLT is one of its cornerstones.

      About other tasks we will else tell in detail and they will then cease to be a secret behind seven seals, but those that we only call and will not reveal to the end, will be very curious. Take for example one problem of astronomers who have accumulated huge collections with records of cosmic signals of electromagnetic radiation from all points of the starry sky. And what to do with them nobody knows. Whether it is the brothers in mind communicate with us or it is just natural radiation. Unmeasured money spent on giant radio telescopes and a bunch of people working for them, but there’s nothing to use. They are simple the poor fellows!

      But we know a way how to distinguish reasonable signals from natural ones, but we will lowly keep silent about this. We know this only because we will reveal here one of the greatest science’s secrets about determining the essence of the information’s phenomenon. It is clear the current science in this matter doesn’t know anything at all. But as soon as we clarify it, then besides us also others can then guess how electromagnetic signals may be analyzed for determining their reasonable origin.

      We'll begin to approach the solution of this problem by penetrating the most important problem of all science, this is defining the essence of the number phenomenon, about which unfortunately science also does not know anything like about many other “simple” questions. And now, when it comes to the most important essence capable of displaying all other essences (yes, yes, it's about number!), we can already see that case is taking a much more serious turn and such shifts are awaiting us, which were not even in the entire visible history of our civilization!!!

      Again, are you in doubt? But that is why you would never guess what are those shifts, and when you find out, you can hardly believe that they are possible, but secrets behind seven seals cannot be other. Until someone gets to them and begins to slowly reveal them, everyone will remain in the dark about how a much is arranged in this world and why it is better to know about it than to live in ignorance about the existence of the wonderful world of science where perfection and precision dominate. And it is just curious to find out how, for example, does look the proofs of the Fermat’s theorems that turned out to be inaccessible even to the greatest scientists. Now there is a book that allows everyone to see with one's own eyes all these hidden and inmost secrets unknown to current science and thereby receive a unique opportunity to rise to a height unattainable before.

      It is enough to see the name Fermat in the title of our work to suppose something great in it. It was such a remarkable man that he could not create anything petty, even average: his mind shone with such a brilliance that he could not tolerate anything dark. It may be said that he is similar to the sun in a moment driving off the dusk and spilling the blinding light of its bright rays even into the abysm. Until now, everyone has been amazed by Diophantus and this is well deserved; but, no matter how great he was, it is a pygmy in comparison with such a giant who has come a long way around the world of mathematics traversed lands that have never been seen before. Vieta was praised by all those who in our century devoted themselves to the study of algebraic operations, so for the glorification of some scientist it was enough to say that in the work on analysis he followed the thoughts of this author. But he also did not reach the heights of science which will become clear from the many examples explained below. Before Claude Gaspar Bachet I always bowed down as before a man of the subtlest mind; in addition, he was a close friend of mine and his research on Diophantus perfectly shows how astute he was in the science of numbers. But his gaze is weaker if you compare it with the lynx eyes of our Fermat, which penetrated into the most intimate depths.

      Jacques de Billy, 1670

      Priest and Professor of Mathematics

      Introduction

      In the content of the book is presented the main

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